[graycat]

You have a good point, but my post was already at the limit of 10,000 characters. Of course the solution to your point is partly a theorem proving course in high school plane geometry and then, finally, a theorem proving course as, say, a college junior in abstract algebra. For such a course, I did say that the last two years should be at a four year institution; at such a school, a good enough course should be available even if the first two years were in a community college where the calculus teaching was poor. Again your point is correct: To learn how to do proofs well enough to be self-sufficient, need at least one theorem proving course where can get homework and tests graded by a competent mathematician.

Don't worry: I've tried to show that P = NP and know that while I've had some candidate ideas I don't have a good idea or a proof. And, I've nearly never written a bad proof; once catch on to how proofs are done, they are surprisingly easy to check for correctness.

Studying is not a full time job -- I was heavily self taught in math and totally self taught in computing and nearly never studied full time. E.g., I read Nearing on linear algebra, Halmos 'Finite Dimensional Vector Spaces', Fleming 'Functions of Several Variables', yes, with the exterior algebra, and much more while working full time in mostly DoD work around DC. I did the research for my Ph.D. dissertation in stochastic optimal control independently in my first summer in graduate school.

Edit: There's a better answer in this thread in

     https://news.ycombinator.com/item?id=6177643